Motivated by the work of [1]}, [2]}, [3]} in this paper, existence along with the interval of existence, uniqueness and continuous dependence of solutions on initial condition have examined for the nonlinear \(\Psi \) -Hilfer FDEs structured as:
\(^H \mathcal {D}^{\eta ,\,\nu \,;\, \Psi }_{a +}y(t)&= f(t, y(t)),~~ ~t \in \Lambda =[a,a+\xi ], ~~\xi >0, ~0<\eta <1, ~0\le \nu \le 1,~\\\mathcal {I}_{a +}^{1-\zeta \,;\, \Psi }y(a)&=y_a \in \mbox{R}, \qquad \zeta =\eta +\nu \left( 1-\eta \right), \) 
